📘 The Science of Un-Mixing Data (PCA & ICA)

Part 1: The Math Toolbox (Prerequisites) Before we can understand PCA and ICA, we need to understand the tools they use. Think of these as the "rules of the game" for handling data. 🔹 Basic Concepts The Matrix (The Table): Data is organized into a matrix, which is just a giant grid of numbers. The columns usually represent different types of measurements (like different microphones or cameras), and the rows represent each specific moment in time we recorded. The Vector (The Arrow): A single row or column from that table is called a vector. Mathematically, a vector is like an arrow pointing to a specific spot in a multi-dimensional space. Inner Product (The Shadow): This is a way to multiply two vectors together. It tells us how much one vector "overlaps" with another. We use this to project our data onto new axes to see it from a better angle. Basis Vectors (The Directions): These are the "original" directions we use to measure things, like the X and Y axes on a graph. 🔹 Statistical